Trigonometry angle of elevation

Question

You go to the Leaning Tower of Pisa and you bring a protractor. With the protractor, you measure that the Tower is leaning at an angle of . You then walk away from the tower 

feet, so that the tower is now leaning towards you.  You measure the angle of elevation to the top of the tower to be .

Write an expression that calculates the distance from the bottom of the Tower to the top of the Tower. Do not evaluate the expression.

feet, so that the tower is now leaning towards you. You measure the angle of elevation to the top of the to.

Answer 1

Draw and label a diagram!

The Tower makes and an angle of 86° with the ground.

The third angle, at the top of the Tower is 31°

h represents the height of the Tower

h / sin 63° = 100 / sin 31°

Answer 2

Form a triangle and use the law of sines. Let ∠A be your position = 63º. Let ∠B be the angle at the top of the tower. Let ∠C = the angle at the base of the tower to the ground = 90-4 = 86º. We know that b is 100 ft. ∠B = 180-63-86 = 31º. Length "a" is the measurement from the top of the tower to the bottom.

Sin(B)/b = Sin(A)/a

a = bSin(A)/Sin(B) = 100Sin(63)/Sin(31)